Self-consistent theory of a homogeneous binary Bose mixture with strong repulsive interspecies interaction

Multicomponent quantum gases are ideal platforms to study fundamental phenomena arising from the mutual interaction between different constituents. Particularly, due to the repulsive interactions between two species, the system may exhibit a phase separation. We develop a mean-field-based theory for a two-component Bose mixture, which is equivalent to the Hartree-Fock-Bogoliubov approximation, and derive analytical expressions for the phase boundary and miscibility. The majority of existing theories, which are valid only for weakly interacting Bose gases, predict that the phase boundary is determined by the criterion $g_{ab}\leqslant\sqrt{g_{aa} g_{bb}}$ (where $g_{ab}$ is a coupling constant between the components $a$ and $b$). We show that in the Bose-Einstein-condensation phase ($T\leqslant T_c$) the system may remain in a stable and miscible phase also for larger values of $g_{ab}$, depending on the gas parameter $\gamma$ and temperature.